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If O is a point within a quadrilateral ABCD show that OA+OB+OC+OD>AC+BD​

Answer 1

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Answer 2

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Samreen

Jan 18, 2015

In a quadrilateral ABCD, show that OA+OB+OC+OD> AC+BD

If O is a point inside a quadrilateral ABCD, show that OA+OB+OC+OD> AC+BD

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Parthasaradhi M

Member since Apr 1, 2017

Given : ABCD is a quadrilateral. O is a point inside the quadrilateral ABCD.

RTP: OA + OB + OC + OD > AC + BD

Construction : Join OA, OB, OC and OD. Also, join AC and BD

Proof : The sum of any two sides of a triangle is always greater than the third side.

In ΔBOD, OB + OD > BD …........(1)

Similarly In ΔAOC, OA + OC > AC ….........(2)

Adding equations (1) and (2), we will get OB + OD + OA + OC > BD + AC

∴ OA + OB + OC + OD > AC + BD